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Classical Potential Theory and Its Probabilistic Counterpart (Broché)

Edition en anglais

  • Springer

  • Paru le : 01/01/2001
Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived... > Lire la suite
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Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later, a new series Ergebnisse der Mathematik und ihrer Grenzgebiete, survey reports of recent mathematical research, was added. Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject.
Springer is reissuing a selected few of these highly successful books in a new, inexpensive softcover edition, to make them easily accessible to younger generations of students and researchers.
  • CLASSICAL AND PARABOLIC POTENTIAL THEORY
    • introduction to the mathematical background of classical potential theory
    • basic properties of harmonic, subharmonic, and superharmonic functions
    • Infima of families of superharmonic functions
    • Potentials on special open sets
    • Polar sets and their applications
    • The fundamental convergence theorem and the reduction operation
    • Green functions
    • The Dirichlet problem for relative harmonic functions
    • Lattices and related classes of functions
    • The sweeping operation
    • The fine topology
    • The Martin boundary
    • Classical energy and capacity
    • One-dimensional potential theory
    • Parabolic potential theory: basic facts
    • Subparabolic, superparabolic, and parabolic functions on a slab
    • Parabolic potential theory (continued)
    • The parabolic Dirichlet problem, sweeping, and exceptional sets
    • The Martin boundary in the parabolic context
  • PROBABILISTIC COUNTERPART OF PART 1
    • Fundamental concepts of probability
    • Optional times and associated concepts
    • Elements of Martingale theory
    • Basic properties of continuous parameter supermartingales
    • Lattices and related classes of stochastic processes
    • Markov processes
    • Brownian motion
    • The Itô integral
    • Brownian motion and Martingale theory
    • Conditional Brownian motion
    • Lattices in classical potential theory and Martingale theory
    • Brownian motion and the PWB method
    • Brownian motion on the Martin space.
  • Date de parution : 01/01/2001
  • Editeur : Springer
  • Collection : Classics in Mathematics
  • ISBN : 3-540-41206-9
  • EAN : 9783540412069
  • Format : Grand Format
  • Présentation : Broché
  • Nb. de pages : 846 pages
  • Poids : 1.37 Kg
  • Dimensions : 15,6 cm × 23,6 cm × 4,8 cm
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Classical Potential Theory and Its Probabilistic Counterpart
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